AP PreCalculus Flashcards: Inverse Functions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
What is the relationship between the domain and range of a function and its inverse?
The domain of a function is the range of its inverse, and the range of the function is the domain of its inverse.
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What is the relationship between the domain and range of a function and its inverse?
The domain of a function is the range of its inverse, and the range of the function is the domain of its inverse.
Given that f(5) = -2 and f is an invertible function, what is the value of f⁻¹(-2)?
The value of f⁻¹(-2) is 5. The input-output pair (5, -2) for f becomes the pair (-2, 5) for f⁻¹.
If an invertible function f has a range of [0, 10] on its domain, what is the domain of its inverse function, f⁻¹?
The domain of the inverse function f⁻¹ is [0, 10], as it is the same as the range of the original function f.
What is an invertible domain?
An invertible domain is a specific interval or set of inputs where a function has an inverse because each output corresponds to only one input in that interval.
What is the result of the composition of a function and its inverse function, such as f(f⁻¹(x))?
The composition of a function and its inverse is the identity function; that is, f(f⁻¹(x)) = x.
How can you use composition to verify that two functions, g(x) and h(x), are inverses of each other?
You must show that both g(h(x)) = x and h(g(x)) = x. If both compositions result in the identity function, the functions are inverses.
What does it mean for a function, f, to be invertible on a specified domain?
A function is invertible on a domain if each output value of f is mapped from a unique input value within that domain.
If the point (a, b) is on the graph of an invertible function f, what corresponding point must be on the graph of its inverse, f⁻¹?
The point (b, a) must be on the graph of f⁻¹, as the input-output pairs of a function are reversed for its inverse.
What is an algebraic method to find the inverse of a function?
The inverse can be found by determining the inverse operations needed to reverse the mapping of the original function.
How do you determine the input-output pairs of the inverse of a function?
To find the input-output pairs of an inverse function, you reverse the input-output pairs of the original function.
What is the identity function in the context of inverse functions?
The identity function is h(x) = x. It is the result of composing a function with its inverse, and it serves as the line of reflection for their graphs.
How is the graph of an inverse function, y = f⁻¹(x), geometrically related to the graph of the original function, y = f(x)?
The graph of the inverse function is a reflection of the graph of the original function over the line of the identity function, y = x.
How can you graphically determine the inverse of a function y = f(x)?
The inverse can be found by reversing the roles of the x- and y-axes, which is visually represented by reflecting the graph of f(x) over the line y = x.
Why is the composition f⁻¹(f(x)) also equal to x?
This composition also results in the identity function (x) because applying the inverse function 'undoes' the operation of the original function, returning the initial input.